The second biggest challenge of computational atomisation is `numerical breakup' of liquid threads. A coarse grid would trigger the formation of thicker numerical threads, and consequently the formation of larger droplets (this problem has been previously reported by [1]}, [2]}, [3]}, and [4]}). [1]} stated that the mesh should be refined up to the point where the dynamics of the thread are solely governed by surface tension forces. These forces would trigger the formation of capillary waves during the retraction of these ligaments, giving rise to the onset of the Rayleigh-Plateau instability (i.e., the `end-pinching' mechanism).
After those mechanisms are initialised, the thread-dynamics enter in an asymptotic behaviour towards the interfacial singularity (i.e., a refined mesh would not affect the size of the resulting droplets). On this basis, the numerical resolution regarding the interfacial length scales will be assessed following the methodology proposed by [6]} and [7]}, who used a `grid-based Weber number', defined by \(We_{\Delta x_{min}} = \rho _{_w} {U^2}\Delta x_{min} / \sigma \) . This equation provides us with the smallest interfacial length scale that the simulation is capable of resolving by assuming that the smallest interfacial structure is equal to the minimum mesh size of the computational domain. [6]} suggested that no further breakup is observed for values under 10. For a Reynolds number corresponding to \(Re \sim 10^4\)  and M3-type mesh, the grid-based Weber number is \(We_{\Delta x_{min}} \sim 4.12\) , which meets the above criterion, suggesting that all
capillary singularities would be resolved.
